A hybrid system which comprises in-plane graphene and hexagonal boron nitride (h-BN) has sparked intense research due to its tailorable and promising physical properties. We have investigated by first-principle calculations the effect of graphene or h-BN domain size on the atomic geometries, electronic properties and thermodynamic properties of graphene/h-BN hybrid systems with a zigzag interface. Lattice dynamics calculations produced no imaginary frequencies suggesting that the structure is dynamically stable regardless of the graphene (h-BN) domain size. However, the band gap and the thermodynamic properties have been demonstrated to be sensitive to the graphene (h-BN) domain size. The band gap, tunable up to 1.01 eV, decreases with the graphene domain size. The Debye temperature responds differently: it increases with the size of the graphene domain. The thermodynamic properties of the hybrid system are bounded by the values for the graphene and h-BN and can be tuned to converge to either the value of graphene or h-BN depending on the size of graphene domain. Detailed chemical and physical insights revealed by this study can pave a way for a more rational design of future nano-devices with optimized electronic and thermal properties.